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User blog:Blueeighthnote/Question of the Day! August 17 ~ 20
The following questions can be answered in the next four days! Hi, everyone! I am Blueeighthnote, and the following questions can be answered until August 21, 12:00 pm (UTC). Questions 1. Which of the following numbers is the smallest? points A) 2^{\tfrac{1}{3}} B) (\dfrac{1}{8})^{-2} C) 2^{-\tfrac{1}{4}} D) (\dfrac{1}{2})^{\tfrac{1}{2}} E) 8^{-\tfrac{1}{3}} 2. The mean of ALPHA and BETA is 28, and the mean of BETA and DELTA is 39. Therefore: ALPHA is than / Equal to / Less than DELTA. points 3. For any number x''', what is the lowest value of 27^{\left ( x^2+\tfrac{2}{3} \right )} ? points 4. In a regular 3-digit number '''xyz, how many numbers in total fit the following criteria: The difference between ones digit (z) and hundreds digit (x) is 2 in absolute value. points Previous Answers (8/14 ~ 16) For number 1: Simply divide 19 by 27. It is equal to 0.703703703...... The 122th digit is equal to the 2nd. Therefore, the answer was 0. For number 2: Using the binomial theorem, \begin{align} 40^{255} &= (39 + 1)^{255} \\ &= {255 \choose 0} 39^{255} + {255 \choose 1} 39^{254} + \ldots + {255 \choose 254} 39 +{255 \choose 255} \\ &= 39k + 1(k \in N)\end{align} Therefore the remainder of 40^{255} is 1. For number 3: \frac{79 * 13 - 97 - 41 - 59}{10} = 83 Leaderboards 1. Blueeighthnote: 13843 points (2 achvmt pkgs) - One more to get the next lucky prime badge! While being the host, the host cannot earn any points during the period. 2. Minipop56: 12206 points - Four more to get the next lucky prime badge! 3. TimBluesWin: 755 points (1 achvmt pkg) 4. Imamadmad: 745 points (1 achvmt pkg) 5. Dalek-James: 730 points 6. Julianthewiki: 525 points (1 achvmt pkg) - RETIRED 7. Lefty7788: 300 points - One more to get the next lucky prime badge! 8. Wikia Contributor 69.235...: 230 points (1 achvmt pkg) 9. Supermario3459: 145 points (1 achvmt pkg) 10. ZombieBird4000: 50 points (1 achvmt pkg) 11. 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